Simplify the following expression: $y = \dfrac{18q - 48}{24q + 18}$ You can assume $q \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $18q - 48 = (2\cdot3\cdot3 \cdot q) - (2\cdot2\cdot2\cdot2\cdot3)$ The denominator can be factored: $24q + 18 = (2\cdot2\cdot2\cdot3 \cdot q) + (2\cdot3\cdot3)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $y = \dfrac{(6)(3q - 8)}{(6)(4q + 3)}$ Dividing both the numerator and denominator by $6$ gives: $y = \dfrac{3q - 8}{4q + 3}$